JAMB - Mathematics (1989 - No. 11)

Find p in terms of q if \(\log_{3} p + 3\log_{3} q = 3\)

(\(\frac{3}{q}\))³

(\(\frac{q}{3}\))^{\(\frac{1}{3}\)}

(\(\frac{q}{3}\))³

(\(\frac{3}{q}\))^{\(\frac{1}{3}\)}

\(\log_{3} p + 3\log_{3} q = 3\)

\(\log_{3} p + \log_{3} q^{3} = 3\)

\(\implies \log_{3} (pq^{3}) = 3\)

\(pq^{3} = 3^{3} = 27\)

\(\therefore p = \frac{27}{q^{3}}\)

= \((\frac{3}{q})^{3}\)